On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra

New arguments proving that successive (repeated) measurements have a memory and actually remember each other are presented. The recognition of this peculiarity can change essentially the existing paradigm associated with conventional observation in behavior of different complex systems and lead towards the application of an intermediate model (IM). This IM can provide a very accurate fit of the measured data in terms of the Prony's decomposition. This decomposition, in turn, contains a small set of the fitting parameters relatively to the number of initial data points and allows comparing the measured data in cases where the “best fit” model based on some specific physical principles is absent. As an example, we consider two X-ray diffractometers (defined in paper as A- (“cheap”) and B- (“expensive”) that are used after their proper calibration for the measuring of the same substance (corundum a-Al2O3). The amplitude-frequency response (AFR) obtained in the frame of the Prony's decomposition can be used for comparison of the spectra recorded from (A) and (B) - X-ray diffractometers (XRDs) for calibration and other practical purposes. We prove also that the Fourier decomposition can be adapted to “ideal” experiment without memory while the Prony's decomposition corresponds to real measurement and can be fitted in the frame of the IM in this case. New statistical parameters describing the properties of experimental equipment (irrespective to their internal “filling”) are found. The suggested approach is rather general and can be used for calibration and comparison of different complex dynamical systems in practical purposes

Spectral-Kinetic Properties and Energy Transfer in Nanoparticles of Y<inf>0.5–x</inf>Ce<inf>0.5</inf>Tb<inf> x</inf>F<inf>3</inf> Solid Solution

© 2020, Springer Science+Business Media, LLC, part of Springer Nature. Crystalline nanoparticles of Y0.5–xCe0.5TbxF3, doped with various concentrations (x = 0, 0.005, 0.01, 0.05, 0.1, 0.15, and 0.2) of Tb3+ ions were synthesized by co-precipitation. The crystal structure and chemical composition of nanoparticles were studied using transmission electron microscopy, scanning electron microscopy, and X-ray diffractometry. The obtained nanoparticles of solid solutions had an elliptical shape with a size of 10–15 nm along the long axis and good crystallinity with the structure of a CeF3 crystal. The spectral-kinetic properties of the obtained nanoparticles, and the effect of the concentration of Tb3+ activator ions on the energy transfer from Ce3+ to Tb3+ ions were investigated. Energy transfer from Ce3+ to Tb3+ ions in nanocrystals of the Y0.5–xCe0.5TbxF3 solid solutions occurs mainly through the dipole–dipole interaction. The results of evaluating the efficiency of energy transfer from Ce3+ to Tb3+ ions show its increase with increasing concentration of Tb3+ ions